Question

In a survey 46,281 women were asked how many children they had.

The results were as follows.

Number of children: 0 1 2     3      4 5   6 7 8 or more

Number of women 12,574 7,493. 11.282 7,124 3,778 1,811  924 523 772

a) P(sampled woman has exactly 4 children)? _______________________

b) P(Sampled woman has more than 3 children)? ___________________

c) Assume this is a simple random sample of U.S. women. Use the Empirical Method to estimate the probability that a woman has more than seven children.

d) Using a cutoff of 0.05, is it unusual for a woman in the survey to have no children?_____________

(Hint: Find the probability the woman has no children.)

Answer 1

a)

P(sampled woman has exactly 4 children) = Number of women with exactly 4 children / Total women in survey

= 3,778 / 46,281

= 0.08163177

b)

P(Sampled woman has more than 3 children) = Number of women with more than 4 children / Total women in survey

= (3,778 + 1,811 + 924 + 523 + 772) / 46,281

= 0.1687085

c)

P(woman has more than seven children) = Number of women with more than 7 children / Total women in survey

= (523 + 772) / 46,281

= 0.02798125

d)

Probability the woman has no children = Number of women with no children / Total women in survey

= 12,574 / 46,281

= 0.2716882

Since the probability the woman has no children is greater than the cutoff of 0.05, it is not unusual for a woman in the survey to have no children.